Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C3 ⋊ #12587 |
794 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^8,3|a^2=e,b^2=f,c^2=h,d^2=h,e^2=h,b^a=bd,d^a=dg,f^a=fh,g^a=gh,c^b=ch,e^b=egh,i^b=i^2,e^d=eh90 conjugacy classes — view the full character table.
| maximal subgroup of | #72247998, #72247999, #72248016, … |
| maximal normal subgroup of | #72247998, #72247999, #72248016, … |
| maximal quotient of | #72271513 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 84555);